What is the key idea behind Dynamic Programming?

What is the key idea behind Dynamic Programming?

• A. Divide and conquer without reuse.
• B. Greedy selection
• C. Solve subproblems independently.
• D. Solve subproblems once and reuse their results to build larger solutions.

Answer: (D)

Dynamic programming hinges on solving subproblems once and reusing their results to build larger solutions. When a problem can be broken into overlapping subproblems, you compute a subproblem’s answer and store it. If the same subproblem comes up again, you fetch the stored result instead of recomputing it. This caching turns many exponential-time tasks into efficient polynomial-time solutions, whether you build up a table iteratively (bottom-up) or solve recursively with memoization (top-down). This approach contrasts with solving subproblems independently or making locally optimal greedy choices without reuse.

Dynamic programming hinges on solving subproblems once and reusing their results to build larger solutions. When a problem can be broken into overlapping subproblems, you compute a subproblem’s answer and store it. If the same subproblem comes up again, you fetch the stored result instead of recomputing it. This caching turns many exponential-time tasks into efficient polynomial-time solutions, whether you build up a table iteratively (bottom-up) or solve recursively with memoization (top-down). This approach contrasts with solving subproblems independently or making locally optimal greedy choices without reuse.